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This work addresses the computational aspects of a model for elastoplastic damage at finite strains. The model is a modification of a previously established model for large strain elastoplasticity described by Perić et al. which is here extended to include isotropic damage and kinematic hardening. Within the computational scheme, the constitutive equations are numerically integrated by an algorithm based on operator split methodology (elastic predictor—plastic corrector). The Newton—Raphson method is used to solve the discretized evolution equations in the plastic corrector stage. A numerical assessment of accuracy and stability of the integration algorithm is carried out based on iso‐error maps. To improve the stability of the local N—R scheme, the standard elastic predictor is replaced by improvedinitial estimates ensuring convergence for large increments. Several possibilities are explored and their effect on the stability of the N—R scheme is investigated. The finite element method is used in the approximation of the incremental equilibrium problem and the resulting equations are solved by the standard Newton—Raphson procedure. Two numerical examples are presented. The results are compared with those obtained by the original elastoplastic model.

According to the microstructural characteristics of composite ceramic, the strain field distribution regularity of triangular symmetrical composite eutectic is obtained from the stress field distribution regularity of three-phase element in composite ceramic. In allusion to the damage of composite eutectic, it is introduced as a variable in this paper with the aim to determine the strain field distribution regularity of triangular symmetrical composite eutectic with damage behavior.

On the basis of the relationship between strain field and fiber inclusions volume fraction, the strain field of composite eutectic is analyzed.

The strain field of composite ceramic is distinctly dependent on the fiber inclusions volume fraction, fiber diameter and damage behavior of composite eutectic by quantitative analysis. The strain in matrix parallel to eutectic is the maximum linear strain and the main factor for the damage and fracture of eutectics.

The foundation of the strength research of composite eutectic is laid.

In structural health monitoring, localization of multiple slight damage without baseline data is significant and difficult. The purpose of this paper is to discuss these issues.

Damage in the structure causes singularities of displacement modes, which in turn reveals damage. Methods based on the displacement modes may fail to accurately locate the slight damage because the slight damage in engineering structure results in a relatively small variation of the displacement modes. In comparison with the displacement modes, the strain modes are more sensitive to the slight damage because the strain is the derivative of the displacement. As a result, the slight variation in displacement data will be magnified by the derivative, leading to a significant variation of the strain modes. A novel method based on strain modes is proposed for the purpose of accurately locating the multiple slight damage.

In the two bay beam and steel fixed-fixed beams, the numerical simulations and the experimental cases, respectively, illustrate that the proposed method can achieve more accurate localization in comparison with the one based on the displacement modes.

The paper offers a practical approach for more accurate localization of multiple slight damage without baseline data. And the robustness to measurement noise of the proposed method is evaluated for increasing levels of artificially added white Gaussian noise until its limit is reached, defining its range of practical applicability.

This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature. Continuum‐based models expressed in terms of softening stress—strain relations, and fracture‐type models expressed in terms of softening stress—displacement relations are distinguished. From one‐dimensional wave propagation calculations, it is shown that strain‐localization into regions of finite size cannot be achieved. The previously well‐documented spurious convergence is obtained with continuum models, while stress—displacement relations cannot model well smeared‐crack situations. Continuum models may, however, be used in general if a localization limiter is implemented. Gradient‐type localization limiters appear to be rather complicated; they require solving higher‐order differential equations of equilibrium with additional bourdary conditions. Non‐local localization limiters, especially the non‐local continuum with local strain, in which only the energy dissipating variables are non‐local, is found to be very effective, and also seems to be physically realistic. This formulation can correctly model the transition between homogeneous damage states and situations in which damage localizes into small regions that can be viewed as cracks. The size effect observed in the experimental and numerical response of specimens in tension or compression is shown to be a consequence of this progressive transition from continuum‐type to fracture‐type formulations.

This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. Such an approach requires C1 continuous approximation. This is achieved by using an isogeometric approximation (IGA). Numerical examples in one and two dimensions are presented.

In this work, the authors propose a nonlocal elastic plastic damage model. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. An additive decomposition of strains in to elastic and inelastic or plastic part is considered. To obtain stable damage, a higher gradient order is considered for an integral equation, which is obtained by the Taylor series expansion of the local inelastic strain around the point under consideration. The higher-order continuity of nonuniform rational B-splines (NURBS) functions used in isogeometric analysis are adopted here to implement in a numerical scheme. To demonstrate the validity of the proposed model, numerical examples in one and two dimensions are presented.

The proposed nonlocal elastic plastic damage model is able to predict the damage in an accurate manner. The numerical results are mesh independent. The nonlocal terms add a regularization to the model especially for strain softening type of materials. The consideration of nonlocality in inelastic strains is more meaningful to the physics of damage. The use of IGA framework and NURBS basis functions add to the nonlocal nature in approximations of the field variables.

The method can be extended to 3D. The model does not consider the effect of temperature and the dissipation of energy due to temperature. The method needs to be implemented for more real practical problems and compare with experimental work. This is an ongoing work.

The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.

The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.

The present work includes the formulation and implementation of a nonlocal damage plasticity model using an isogeometric discretization, which is the novel contribution of this paper. An implicit gradient enhancement is considered to the inelastic strain. During inelastic deformations, the proposed strain tensor partitioning allows the use of a distinct potential surface and distinct failure criterion for both damage and plasticity models. The use of NURBS basis functions adds to more nonlocality in the approximation.

The purpose of this paper is to present a methodology to assess material damage parameters for ductile crack initiation and growth ahead of a crack/notch tip in high hardening steel like AISI type 316L(N) stainless steel.

Ductile damage parameter and far field J-integral have been obtained from standard FEM analysis for a crack/notch tip undergoing large plastic deformation and resulting in crack initiation/growth. In conjunction with experimental results, the damage variable for low strength and high hardening material has been derived in terms of continuum parameters: equivalent plastic strain (ε_eq) and stress triaxiality (φ). The material parameters for damage initiation and growth in 316LN SS have been evaluated from tensile and fracture tests. With these material tensile/fracture parameters as input, elastic-plastic eXtended Finite Element Method (X-FEM) simulations were carried out on compact tension (CT) specimen geometry under varying initial stress triaxiality conditions.

The material parameters for damage initiation and growth have been assessed and calibrated by comparing the X-FEM predicted load-displacement responses with the experimental results. It is observed that the deviations in the predicted load values from the experimental data are within 6 percent for specimens with a/W=0.39, 0.55, 0.64, while for a/W=0.72, it is 17 percent.

The present study is a part of developing methods to obtain calibrated material damage parameters for crack growth simulation of components made of AISI 316L(N) stainless steel. This steel is used for fast breeder reactor-based power plant being built at Kalpakkam, India.

During the running of automobile, the stabilizer bar is frequently subjected to the impact of complex random loads, which is prone to fatigue failure and accident. In regard to this, the purpose of this paper is to study and discuss fatigue life of automobile stabilizer bar.

Durability bench test shows that failure is located at the joint of sleeve and stabilizer bar body. Based on the collection and compilation of micro-strain load spectrum of the stabilizer bar, the strain-life model is studied considering the influence of average stress and maximum stress at failure area. Seven-grade strain-life curves of the stabilizer bar are established. According to the principle of linear damage accumulation, the relationship between fatigue life and damage is discussed, then the fatigue life of stabilizer bar is predicted. Fatigue life evaluation is carried out from three aspects: reliability analysis, static analysis and fatigue life simulation.

The results show that the reliability of the test sample is 99.9 percent when the confidence is 90 percent and the durability is 1,073 load spectrum cycles; the ratios of predicted and simulated life to design life are 2.77 and 2.30, respectively.

Based on the road load characteristics of automobile stabilizer bar, the method of fatigue life prediction and evaluation is discussed, which provides a basis for the design and development of automobile chassis components.

The paper aims to present a modeling method for multi‐layer, multi‐material printed circuit boards (PCBs) in both micro‐structure and board levels.

The method incorporates a multilayer finite element model that is established in two parts: the first part is an elasto‐plastic damaging model, which is presented to model metallic plies in the multi‐layer PCBs, while the second is a bi‐phase model for glass‐fiber/epoxy‐resin composite ply with fiber/matrix structure.

Numerous composite parts and complex material properties of multi‐layer PCBs complicate the reliability of the simulation. Therefore, the board level simulation and the micro‐structure modeling cannot be performed at the same time. A multi‐layer FEM code can solve this problem: with the use of bi‐phase and elasto‐plastic plies in this code, the micro‐structure and board‐level modeling for multi‐layer PCBs can be incorporated.

With the implementation of a virtual boundary method, the current multi‐layer model can be combined with the unit‐cell modeling method to perform detailed analysis at the micro‐structure level.

This paper presents a method for multi‐layer PCB modeling at both the micro‐structure and board levels. It provides a way to individually design the fabric types and the properties of glass fibers, epoxy resin, and copper foil in PCBs, to meet specific reliability requirements. With the proposed modeling, the static and shock responses of optimized PCBs can be analyzed with less computation.

Simple but also accurate models are needed to predict the failure response of concrete structures. Simplicity involves modelling assumptions while accuracy involves objectivity of both the experimentally identified model parameters and the numerica results. For concrete‐like heterogeneous and brittle materials, the modelling assumptions idealizing the material as a homogeneous continuum with classical linear or non‐linear behaviour, leads to some problems at the identification stage, namely the size effect phenomena. A continuum damage model, representing the non‐linear behaviour due to microcracking, is proposed here for predictive computations of structural responses. A Weibull based theory is used to determine, in a statistical sense, the value of the initial damage threshold. The essential influence of material heterogeneity on the damage evolution, is accounted for with a bi‐scale approach which is based on the idea of the non‐local continuum with local strain. It has already established that the non‐local approaches yield realistic failure predictions and the numerical results are convergent for subsequent mesh refinements. The applications presented here show the ability of the approach to predict the failure response of concrete structures without being obscured by size effect problems.

Focuses on a finite element computational model for the Timoshenko beam which is idealized as an elasto‐plastic‐damage medium governed by Lemaitre’s continuum damage mechanics (CDM) model for ductile fracture. Response under monotonically increasing loading does not show any deviation from elasto‐plastic simulation. However, a marked difference in the residual stress field is noted by virtue of the unloading phase, in which the CDM model allows for stiffness degradation in contrast to classical elasto‐plasticity which requires unloading at the (frozen) initial stiffness of the material.